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3 years ago

The radius of a sphere X is 3 inches, and radius of sphere Y is 9 inches. How many

Mathematics

1 answer:

kirza4 [7]3 years ago

7 0

The volume of the sphere Y is 27 times the volume of the sphere X

Step-by-step explanation:

Sphere X:

Radius of sphere X = 3 inches

Volume = (4/3) π(27)

Sphere Y:

Radius of sphere Y = 9 inches

Volume = (4/3) π(729)

Volume of sphere Y /volume of sphere X = (4/3) π(729) /(4/3) π(27)

= (729) /(27)

= 27

The volume of the sphere Y is 27 times the volume of the sphere X

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A hamster running in a wheel of radius 13 cm spins the wheel at 35 revolutions per minute.

crimeas [40]

One revolution is completed when a fixed point on the wheel travels a distance equal to the circumference of the wheel, which is 2π (13 cm) = 26π cm.

So we have

1 rev = 26π cm

1 rev = 2π rad

1 min = 60 s

(a) The angular velocity of the wheel is

(35 rev/min) * (2π rad/rev) * (1/60 min/s) = 7π/6 rad/s

or approximately 3.665 rad/s.

(b) The linear velocity is

(35 rev/min) * (26π cm/rev) * (1/60 min/s) = 91π/6 cm/s

or roughly 47.648 cm/s.

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3 years ago

Simplify 20+4(3)÷(-8)

Mashcka [7]

The answer to this problem would be 12. If you need to show work just comment.

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2 years ago

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Sami took six quizzes in science class. The grades for the quizzes are 86, 92, 79, 96, 80, and 95. What is the median grade?

mart [117]

Answer:

The median grade would be 89

Step-by-step explanation:

To find the median, first put the numbers all in ascending order.

79, 80, 86, 92, 95, 96

Now isolate the middle term or terms. Since there is an even amount of numbers, we pick the two in the middle. To find the median, we take an average of those terms.

(86 + 92)/2 = 89

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3 years ago

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Solve the system: 2/x - 3/y =-5; 4/x + 6\y =14

sertanlavr [38]

The solution is $x = 2 \text{ and } y = \frac{1}{2}$

Solution:

Let us assume,

$a = \frac{1}{x}\\\\b = \frac{1}{y}$

Given system of equations are:

$\frac{2}{x} - \frac{3}{y} = -5$

$\frac{4}{x} + \frac{6}{y} = 14$

Rewrite the equation using "a" and "b"

2a - 3b = -5 ------------ eqn 1

4a + 6b = 14 -------------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

2(2a - 3b = -5)

4a - 6b = -10 ------------- eqn 3

Add eqn 2 and eqn 3

4a + 6b = 14

4a - 6b = -10

( - ) --------------------

8a = 4

$a = \frac{4}{8}\\\\a = \frac{1}{2}$

Substitute a = 1/2 in eqn 1

$2(\frac{1}{2}) -3b = -5\\\\1 - 3b = -5\\\\3b = 6\\\\b = 2$

Now let us go back to our assumed values

Substitute a = 1/2 in assumed values

$a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2$

Substitute b = 2 in assumed value

$b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}$

Thus the solution is $x = 2 \text{ and } y = \frac{1}{2}$

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